Mathematical Poise and Movement in Thinking: The Zero Goes on Vacation
Johnson, Shirley M. Langham
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https://hdl.handle.net/2142/65960
Description
Title
Mathematical Poise and Movement in Thinking: The Zero Goes on Vacation
Author(s)
Johnson, Shirley M. Langham
Issue Date
1980
Department of Study
Education
Discipline
Education
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Education, Mathematics
Language
eng
Abstract
This is a clinical case study that describes mathematical thinking of a seven year old girl, Kay. It reports analyses of video-taped clinical interviews using Piagetian tasks of conservation, number and numeral and other number tasks. It includes a report of microanalysis of one interview, called the Odometer video-tape. Generally, the report attempts a fairly well-rounded portrait of Kay, as a child who customarily thinks about numbers with exceptional poise or equanimity.
"The main thrust of the study is to address the question of how cognitive structures may be described as occurring and as moving within Kay's consciousness (e.g., as she talks about numerals moving on the dial of the mileage indicator of an imaginary car). The study generates several notions that may be useful in describing the occurrence of cognitive structures within consciousness. These are designated as the mind's eye, virtual-thinking, change points, marshaling, flashing, purposefully directed intent, and spanning. The study raises several questions for research and for schooling, exploring one such question in depth, ""How can schooling facilitate the development in students, generally, of the kind of mathematical poise observed in Kay?"""
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